Primark has begun the process of paying compensation to thousands of workers and their families who were involved in the Rana Plaza factory disaster, as campaigners said retailers must do more to protect workers' rights.

The high-street clothes chain, whose supplier Simple Approach occupied the second floor of the eight-storey Rana Plaza building that collapsed in April, has promised money will start flowing into the bank accounts of almost 4,000 workers or their dependents next week.

Primark, whose owner Associated British Foods reported bumper half-year pre-tax profits of £415m in April, said it was spending $1m (£640,000) on short-term aid for victims. "It is the right thing to do," said Paul Lister, head of governance at AB Foods. "There is obviously real hardship, short-term hardship, which we initially dealt with with food aid."

The company had decided to provide short-term aid, equivalent to three months' wages, because long-term compensation "will take a period of time to deal with and in the meantime some of these people are suffering real hardship".

The Rana Plaza factory collapse was the worst garment disaster in history, leaving 1,129 dead and many hundreds with devastating injuries, including lost limbs.

Lister said the retailer didn't know how long it would take to deliver long-term aid to victims. "That is a discussion that will take a while. History says it could take a long period of time. We would not expect it to take as long as it has in the past. We will work really hard to make sure that this doesn't happen."

After previous factory disasters, victims and their families have waited up to two years for compensation. Primark, whose supplier employed less than 10% of the Rana Plaza workforce, has pledged compensation to all victims. The company, with the help of a local non-governmental organisation, has set up bank accounts for victims to avoid money being siphoned off by unscrupulous middlemen.

Peter McAllister, executive director of the Ethical Trading Initiative, which brings together firms, trade unions and NGOs, said identifying victims was an "incredibly complicated" business. A company has to weed out false claims and trace victims who had returned to their villages, as well as deal with weak government structures.

Daniel Randall, an activist with the No Sweat campaign, said the compensation deal was "certainly better than nothing", but Primark still had "a long way to go".

"The fundamental thing we want is for companies to recognise independent trade unions in the workplace, for without the right to organise collectively no amount of legislation will ever be enforceable, it's only going to be so many words on a piece of paper.

"If Primark wants to guarantee that compensation gets to the right place and that any health and safety accords are properly enforced, the way to do that is to give their workers space to organise and ensure independent trade unions can do that in every factory."

Randall acknowledged that companies are not the only factor affecting workers' rights. "There is a wider question about labour law in Bangladesh and other countries and government hostility to independent unions."

Randall pointed out Gap and Walmart for refusing to sign the accord on fire and building safety in Bangladesh, an agreement drawn up by unions and campaigners with the support of more than three dozen retailers, including H&M, Zara-owner Inditex, Marks & Spencer and Primark.

"The very fact that they have refused to acknowledge the legitimacy of the accord … illustrates a contempt for workers' agency," he said.

A spokesman for Walmart, which owns Asda, said the company had taken "a number of actions that meet or exceed other factory safety proposals", such as strengthening factory standards, zero-tolerance of unauthorised subcontracting and in-depth safety audits. Gap did not immediately respond to a request for comment.